Question about false positives?

In January of last year, I finally got a positive test after 1.5 years of TTC. I had a positive internet cheapie, a positive first response (both very faint) and a positive digital as well.

I ended up getting my period 1 week after the initial faint positive on the internet cheapie. I assumed it was a chemical pregnancy.

But now its been another year, and nothing else has happened.

So, I've just been wondering, was I even pregnant? Or could these have been false positives? Doesn't implantation need to occur in order to get a positive test? I'm starting to doubt that it even happened since it hasn't happened again. Sorry if this is a dumb question but I just want some reassurance that this did happen, it will give me some hope that it can happen again.